Method and apparatus for enhancing in-situ gas flow measurement performance

ABSTRACT

An in-situ gas flow measurement controller measures the temperature and rate of pressure drop upstream from a flow control device (FCD). The controller samples the pressure and temperature data and applies the equivalent of a decimating filter to the data to produce filtered data at a slower sampling rate. The controller derives timestamps by counting ticks from the sampling clock of the A/D converter that is sampling the pressure at regular intervals to ensure the timestamps associated with the pressure samples are accurate and do not contain jitter that is associated with software clocks. The controller additionally normalizes the temperature reading to account for power supply fluctuations, filters out noise from the pressure and temperature readings, and excludes data during periods of instability. It calculates the gas flow rate accounting for possible non-linearities in the pressure measurements, and provides the computed gas flow measurement via one of many possible interfaces.

BACKGROUND

1. Field of the Invention

The subject invention relates to gas flow measurement

2. Related Art

The accurate flow of gas is important in many industrial processes. Inthe semiconductor industry, transistor critical dimensions are evershrinking to smaller and smaller technology nodes. As the criticaldimension requirements become tighter, it is becoming increasinglyimportant to improve the precision of the wafer processing to enable thefabrication of semiconductor chips at smaller nodes. For recipes thatare dependent on an accurate flow of gases, the ability to measure theaccurate flow rate of individual gases into the process chamber isextremely important.

Several solutions that allow for the measurement of gas flow into aprocess chamber have been developed as a response to the market need.However, most of the solutions do not allow for the accurate measurementof gas flows during chamber processing. Patent application Ser. Nos.12/354,723 and 12/355,654 by Monkowski et al, describe a novel solutionthat allows for in-situ gas flow measurement of individual gases flowinginto a process chamber. The solution describes the method of stoppingthe flow of gas upstream of a gas stick's flow control device (generallya mass flow controller) and measuring the rate of pressure drop in thevolume between the location where flow has been stopped and the flowcontrol device in order to calculate a flow rate.

The precision of prior art in-situ gas flow measurement is highlydependent upon the pressure reading from a pressure measurement device.Thus, prior art systems may provide accurate measurements inwell-controlled environments. However, in less controlled environments,noise or other anomalies in the pressure measurement can adverselyaffect the gas flow calculation, decreasing its reliability andrepeatability. Similarly, noise or an offset in the temperature readingcan also affect the accuracy and repeatability of the gas flowcalculation.

When taking pressure measurements, the accuracy of the timestampsassociated with the samples can affect the gas flow measurement, sincewhen calculating rate of pressure drop the accuracy of the sampletimestamps are as important as the accuracy of the pressure readings.The issue is further complicated since it is commonly known that typicaltool and chamber controller operating system software clocks havemargins of error on the order of a few milliseconds, which could affectthe gas flow measurement calculation significantly.

Additionally, non-linearities and discontinuities in the gas pressurereadings due to set point changes or non-ideal gas compressibilityfactors may cause inaccuracies in gas flow measurements. Novel methodsas described in the detailed description below can be employed toaccount for such non-linearities and discontinuities in order to providemore accurate gas flow measurement results.

From the above, it is seen that techniques for enhancing the robustnessand performance of in-situ gas flow measurement systems are desired.

SUMMARY

The following summary is included in order to provide a basicunderstanding of some aspects and features of the invention. Thissummary is not an extensive overview of the invention and as such it isnot intended to particularly identify key or critical elements of theinvention or to delineate the scope of the invention. Its sole purposeis to present some concepts of the invention in a simplified form as aprelude to the more detailed description that is presented below.

Embodiments of the present invention employ an in-situ gas flowmeasurement (GFM) controller that measures the temperature and rate ofpressure drop upstream from a flow control device (FCD). The GFMcontroller samples the pressure and temperature data and applies theequivalent of a decimating filter to the data to produce filtered dataat a slower sampling rate. The GFM controller derives timestamps for thepressure samples by counting ticks from the sampling clock of theanalog-to-digital converter that is sampling the pressure at regularintervals to ensure the timestamps associated with the pressure samplesare accurate and do not contain jitter that is associated with softwareclocks. The GFM controller additionally normalizes the temperaturereading to account for power supply fluctuations, filters out noise fromthe pressure and temperature readings, and excludes data during periodsof instability. It then calculates the gas flow rate accounting forpossible non-linearities in the pressure measurements, and provides thecomputed gas flow measurement via one of many possible interfaces.

According to aspects of the invention, a method of computing the rate atwhich gas flows out of a processing chamber gas stick is provided, themethod comprising: stopping the flow of gas into the gas stick at afirst location which is upstream of a second location where gas isflowing out of the gas stick, obtaining a plurality of measurements, ata first sampling rate, of the gas in a volume in fluid communicationwith, and located in between, said first and second gas stick locations,obtaining a voltage reading of a power supply of a sensor providing saidmeasurements, normalizing said measurements with said voltage reading,performing a gas flow calculation, where the gas flow calculationincludes using at least two normalized measurements to compute the rateof gas flow out of said volume by calculating the rate of decrease inmoles of the gas in the volume using a derivative of the ideal gas law,and providing the results of the gas flow calculation via a systeminterface.

According to further aspects of the invention, a method of computing therate at which gas flows out of a processing chamber gas stick isprovided, the method comprising: stopping the flow of gas into the gasstick at a first location which is upstream of a second location wheregas is flowing out of the gas stick, obtaining a plurality ofmeasurements, at a first sampling rate, of the gas in a volume in fluidcommunication with, and located in between, said first and second gasstick locations, filtering the measurements to produce filtered data ata second sampling rate, performing a gas flow calculation, where the gasflow calculation includes using at least two filtered data points tocompute the rate of gas flow out of said volume by calculating the rateof decrease in moles of the gas in the volume using a derivative of theideal gas law, and providing the results of the gas flow calculation viaa system interface.

According to yet further aspects of the invention, a method of computingthe rate at which gas flows out of a processing chamber gas stick isprovided, the method comprising: stopping the flow of gas into the gasstick at a first location which is upstream of a second location wheregas is flowing out of the gas stick, obtaining a plurality ofmeasurements of the gas in a volume in fluid communication with, andlocated in between, said first and second gas stick locations, applyingone or more criteria to determine if any measurements should be excludedfrom gas flow calculation, excluding any measurements from gas flowcalculation that meet said criteria, performing a gas flow calculation,where the gas flow calculation includes using at least two non-excludedmeasurements to compute the rate of gas flow out of said volume bycalculating the rate of decrease in moles of the gas in the volume usinga derivative of the ideal gas law, and providing the results of the gasflow calculation via a system interface.

According to yet further aspects of the invention, a method of computingthe rate at which gas flows out of a processing chamber gas stick isprovided, the method comprising: stopping the flow of gas into the gasstick at a first location which is upstream of a second location wheregas is flowing out of the gas stick, obtaining a plurality ofmeasurements, at a first sampling rate, of the gas in a volume in fluidcommunication with, and located in between, said first and second gasstick locations, deriving time-stamps for said measurements, performinga gas flow calculation, where the gas flow calculation includes using atleast two measurements and their corresponding derived time-stamps tocompute the rate of gas flow out of said volume by calculating the rateof decrease in moles of the gas in the volume using a derivative of theideal gas law, and providing the results of the gas flow calculation viaa system interface.

According to yet further aspects of the invention, a method of computingthe rate at which gas flows out of a processing chamber gas stick isprovided, the method comprising: stopping the flow of gas into the gasstick at a first location which is upstream of a second location wheregas is flowing out of the gas stick, obtaining a plurality ofmeasurements of the gas in a volume in fluid communication with, andlocated in between, said first and second gas stick locations, obtainingcompressibility factors of the gas that correspond to the values of saidmeasurements, scaling said measurements by their correspondingcompressibility factors, performing a gas flow calculation, where thegas flow calculation includes using at least two scaled measurements tocompute the rate of gas flow out of said volume by calculating the rateof decrease in moles of the gas in the volume using a derivative of theideal gas law, and providing the results of the gas flow calculation viaa system interface.

According to yet further aspects of the invention, a gas flowmeasurement system is provided, which is coupled to a gas stick in fluidcommunication with a processing chamber, the gas stick comprising a flowcontrol device on the gas stick located upstream of the processingchamber, a valve, on the gas stick, located upstream of the flow controldevice, which has the ability to regulate the flow of gas through thegas stick, and a volume in fluid communication with, and located inbetween, the valve and the flow control device, the system comprising:one or more sensors in fluid communication with, and located in between,the valve and the flow control device, and, a computer, in electroniccommunication with said sensors, and which comprises: a processor, acomputer-readable medium having stored thereupon a program that, whenexecuted on said processor causes the processor to perform any of themethods of the invention. For example, according to one implementation,the program causes the processor to perform steps: stop the flow of gasinto the gas stick by turning off the valve, obtain a plurality ofmeasurements, at a first sampling rate, of the gas in the volume, obtaina voltage reading of a power supply of the one or more sensors providingsaid measurements, normalize said measurements with said voltagereading, perform a gas flow calculation, where the gas flow calculationincludes using at least two normalized measurements to compute the rateof gas flow out of said volume by calculating the rate of decrease inmoles of the gas in the volume using a derivative of the ideal gas law,and provide the results of the gas flow calculation via a systeminterface.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a simplified block diagram of a gas flow monitor system forimplementing embodiments of the invention.

FIG. 2 is a block diagram of an alternate embodiment of a gas flowmonitor system.

FIG. 3 is a simplified block diagram of a sample temperature sensor forimplementing embodiments of the invention.

FIG. 4 is a simplified block diagram of a sample temperature sensor withanalog normalization according to an embodiment of the invention.

FIG. 5 is a simplified block diagram of a sample temperature sensor withdigital normalization according to an embodiment of the invention.

FIG. 6 is an example of high level process flow for GFM calculationaccording to an embodiment of the invention.

FIG. 7 is an example of modified high level process flow for GFMcalculation where sampling rate is faster than GFM processing rate,according to an embodiment of the invention.

FIG. 8 is a high level process flow for deriving accurate timestamps forGFM data samples according to an embodiment of the invention.

DETAILED DESCRIPTION

Embodiments of the present invention employ a gas flow measurement (GFM)controller that measures the rate of gas flow through a gas stick into aprocessing chamber. FIG. 1 shows a GFM controller in a system 100 inaccordance with the present invention. The system comprises a gas box104 that contains a gas stick 106 which regulates the gas flow from thegas source 102 into the process chamber 108. The gas stick 106 containsa valve 110 which can regulate the flow of gas into the gas stick, atemperature sensor 112 that can measure the approximate temperature ofthe gas, a volume 114 which comprises the internal volume of the gasstick in between the valve 110 and the flow control device 118, apressure sensor 116 which can measure the pressure of the gas within thevolume 114, and a flow control device 118 (e.g., a conventional massflow controller) which regulates the flow of gas out of the volume 114.A GFM controller 120 receives a notice via communications link 132signaling when the gas stick is in a state where the valve 110 has beenshut to prevent any gas from entering the volume 114, but the flowcontrol device 118 is flowing gas out of the volume 114. The GFMcontroller 120, through execution of the GFM software 126, takes one ormore temperature measurements over communications link 128, and at leasttwo pressure readings over communication link 130 (which may be the samelink), and uses them to calculate the flow rate of gas out of volume114.

The temperature reading communications link 128 and the pressure readingcommunications link 130 can take the form of analog circuit connections,where the measurements are transmitted in the form of voltage levelsover analog lines. Alternatively, the communication links can take theform of digital wired or wireless communication links, wheremeasurements are transmitted using digital protocols such as a paralleldigital bus, RS-232, RS-485, Ethernet, CanBus, WiFi, and Bluetooth,among others. Similarly, GFM controller communications link 132 can takethe form of an analog line or a digital communications link, andprovides the ability for an external entity (usually the chambercontroller) to inform the GFM controller 120 when the gas stick is in astate where the gas flow measurement can be performed using the pressurerate of drop as described above. Additionally, the GFM controllercommunications link 132 has the ability to provide the results of thegas flow measurement back to the external entity.

FIG. 2 shows an alternate embodiment with additional communicationslinks. In this embodiment, the GFM controller uses a communications link236 to control the valve 110. It also uses communications link 230 toobtain a feedback reading from the FCD 118. In addition, it has aseparate communications link 234 for providing gas flow measurementoutput to a separate external entity than the one in communication vialink 132. In either embodiment, the communications links 132 and 234 cantransmit information in the form of analog voltages, or via digitalinterfaces such as a parallel digital bus, RS-232, RS-485, Ethernet,CanBus, Profibus, and wireless protocols, among others.

Although the above embodiments are sufficient for obtaining an estimateof the gas flow rate out of volume 114, certain errors introduced in themeasurement and sampling of the temperature and pressure can reduce theaccuracy and repeatability of the gas flow measurement. The equationused by the GFM software 126 to calculate the gas flow rate is asfollows as taught by Monkowski et al (derived from the ideal gas law):

n=PV/RT, where   Equation (1)

n=amount of gas

P=pressure

V=volume

R=ideal gas constant

T=temperature

By measuring the change in the variable n over time, we can determinethe amount of gas leaving volume 114, thus computing the flow rate ofgas out of volume 114. Thus, the flow rate f can be calculated with thefollowing formula:

$\begin{matrix}{{{f = {\frac{\Delta \; n}{\Delta \; t} = \frac{\Delta ( {{PV}/{RT}} )}{\Delta \; t}}},{where}}{f = {{flow}\mspace{14mu} {rate}}}{t = {time}}} & {{Equation}\mspace{14mu} (2)}\end{matrix}$

In the above equation, it can be seen that if some errors are introducedinto the pressure, temperature, or time measurements, the resulting flowrate calculation is undesirably affected.

Temperature Input Data Error Correction

FIG. 3 illustrates an example temperature sensor for use in accordancewith the present invention. Temperature sensor 300 employs an electricalcircuit 302 and a supply of power 308 to convert readings from atemperature sensing element 304 into an analog temperature signal 310.Optionally, the temperature sensor 300 can digitize the analogtemperature signal 310 using an ADC, or provide the output as an analogsignal and let the GFM controller 120 digitize it using its own ADC.

One source for error in the measurement of temperature is noise in theanalog temperature signal 310 which can come from a variety of sources,including but not limited to noise in the power supply 308,electro-magnetic interference from external sources, or aliasing ofnoise during sampling. When the analog temperature signal 310 isdigitized, the differences in readings caused by the noise level at thetime of the sampling may introduce artificial fluctuations in thedigitized values, therefore introducing an artificial fluctuation in thegas flow calculation.

One embodiment of the present invention makes use of the observationthat it is uncommon for the temperature on a gas stick to changeradically over a short period of time. Therefore a low pass filter isapplied to the temperature measurement signal to safely filter outartificial fluctuations without adversely affecting the temperaturereading. In the case where the noise is periodic, a filter lengthintegral to the period of the noise is used to filter out the periodicnoise.

Another source for error in the temperature measurement is caused by theproportional relationship between power supply 308 voltage and analogtemperature signal 310. Namely, since the temperature circuit 302 isusing power supply 308 to provide an analog temperature output 310, theanalog temperature output 310 will rise and fall proportionally to therise and fall of the power supply 308 voltage. Thus, if a gas stickemploys a first temperature sensor using a first power supply, and thesame gas stick employs a second temperature sensor using a second powersupply, unless the voltage output of the two said power supplies areidentical, the temperature readings of the two temperature sensors willdiffer proportionally to the difference in power supply voltages. Forexample, if the first power supply provided a nominal voltage of 9.75V,while the second power supply provided a nominal voltage of 10.25V, theresulting temperature readings will differ by an amount proportional to0.5V (the difference between 10.25V and 9.75V), even when both sensingelements are measuring the exact same temperature. Even if bothtemperature sensors were calibrated to adjust for the difference inpower supply voltage, the voltage of the power supply can fluctuate overtime, again resulting artificial fluctuations in the gas flowmeasurement.

Embodiments of the present invention provide for normalizing thetemperature readings to account for changes in power supply voltagelevels. FIG. 4 illustrates a high level block diagram of a system 400that enhances a temperature circuit 300 to provide a normalizedtemperature reading that accounts for the variances in nominal voltageoutput from power supplies 308. A divider 402 performs the equivalent ofarithmetically dividing the temperature signal 310 by the power supplysignal 410 to create a normalized temperature signal 412.

FIG. 5 shows an alternate embodiment that allows for the normalizationto take place after the data has been digitized. In this embodiment,analog-to-digital converters are used to digitize the power supply andtemperature signals to produce a digitized power supply signal 510 and adigital temperature signal 512. A processor 506 then divides the digitaltemperature signal 512 by the power supply signal 510 to produce anormalized digital temperature signal 514.

In either embodiment, the normalization process will result in anormalized temperature signal that is of a different scale than theun-normalized temperature signal. This can be corrected by multiplyingthe normalized temperature signal by an appropriate constant. In somecases, these normalization techniques are also applicable to other dataused by the GFM system, such as pressure data. For example, the powersupply voltage of the pressure sensor 116 could be used to normalize thepressure readings using the same techniques described above.

Pressure Input Data Error Correction

The gas flow calculation is also susceptible to noise in the pressurereadings. Similar to the temperature readings, noise in the powersupply, electro-magnetic interference from external sources, or aliasingof noise during sampling, for example, could create inaccuracies in thepressure readings. One solution is to average pressures samples over arolling window. However, unlike temperature, the pressure is expected tochange materially over a short period of time, and it is desirable tomonitor that change. Therefore averaging or applying a low-pass filtermay result in filtering out some of the pressure signal instead ofnoise. In addition, filtering the pressure signal digitally would createa delay in the pressure reading proportional to the length of thefilter, resulting from a delayed gas flow measurement. For someapplications a delay in the gas flow measurement is acceptable, but forapplications that require real-time data (such as when it is used in areal-time control loop), a delay in the gas flow measurement may beunacceptable.

Embodiments of the present invention allow for over-sampling pressuredata at a rate faster than the desired data rate at which the GFM systemprocesses data, applying a decimating filter to the raw data to producefiltered data at the desired data rate, and using the filtered data inthe GFM calculations. In one embodiment, a filtered data sample isproduced by averaging over-sampled data points obtained since theprevious filtered data sample. For example, consider the situation whereit is desired to provide GFM measurements using pressure data at 20 Hz(i.e., one sample every 50 ms). However, rather than sampling pressuredata at 20 Hz, the pressure data is over-sampled at a faster rate of 4KHz (i.e., once every 0.25 ms), which allows for averaging 200 pressuresamples in order to produce each averaged sample, resulting in averagedpressure data at 20 Hz. The gas flow calculation is then performed onthe 20 Hz filtered data, which results in the desired level of timegranularity. One skilled in the art would see show other variations ofdecimating filters can be applied to achieve similar results. Thistechnique gives the gas flow measurement system a method for filteringout noise, without incurring any additional delay in the gas flowmeasurement output.

FIG. 6 illustrates a high level process flow for calculating gas flowmeasurements without the method above. The system 600 begins processing611 by entering into a loop 612 in which pressure samples are taken 613and added to a collection 614. The collection of data points isprocessed 615, and if a sufficient number of points have been collected,a gas flow measurement is computed and optionally provided as output616. FIG. 7 shows a high level process flow of the same example exceptwith the added innovation of sampling data faster than it is beingprocessed—200 times faster in the illustrated example. The flow ofsystem 600 is enhanced by replacing step 613 with process 700, where 200data samples are collected 713 at a faster rate of 0.25 ms, and thenaveraged 716 to create an averaged data sample that is used for gas flowmeasurement calculation 615. Although this technique is described forpre-processing pressure data, in some cases it is also applicable toother data that the GFM system collects. For example, temperature datacan be over-sampled in order to average out noise using the techniquesdescribed above.

Accurate Time-Stamping of Input Data

For the purposes of describing the invention, an “oscillator” is hereinreferred to as a device that produces a hardware timing signal, such asa CPU clock. A “system clock” is referred to as a module that keeps dateand time, such as the system clock maintained by a computer operatingsystem. The “system time” is the date and time kept by the system clock.A “gas flow measurement period” is a duration during which gas flowmeasurements are to be computed. Typically on a semiconductor tool, thegas flow measurement period either coincides with the duration of arecipe step or it takes place during the first several seconds of arecipe step.

Another source of error in the pressure measurements is not related tothe value of the pressure measurement, but rather to the time-stampingof the measured value. Since the gas flow calculation requires thecomputation of the rate of change of pressure, an error in thetime-stamp of a pressure sample can produce a proportional error in thegas flow measurement. A typical pressure sensor used on gas sticks inthe semiconductor industry provides a pressure measurement as an analogoutput. It is then up to the GFM controller to digitize the analogpressure signal using an ADC and apply a time-stamp to the sample.Conventionally, in such situations a time-stamp is derived by looking upthe current time from the system clock at the moment the sample isdigitized by the ADC.

This conventional method of deriving a timestamp can often yieldtime-stamps that are not as accurate as desired, since the system timemaintained by a computer operating system is typically only accurate toa few milliseconds. However, when the sampling rate is high, a fewmilliseconds of inaccuracy can become a first order source of error inthe gas flow calculations. For example, if the GFM controller samplesthe pressure data at once every 50 ms., a 5 ms error in the time-stampcan result in a 10% error in a 2-point slope calculation.

Embodiments of the present invention allow for the use of a hardwareoscillator to accurately time-stamp the samples from the pressuresensor. One embodiment makes use of the observation that for gas flowmeasurement computation, relative time is more important than absolutetime. That is, it is acceptable for the timestamps to have a constantoffset from an atomic time source (such as the NIST atomic clock), butit is not acceptable if there is relative time error between twopressure samples used for the gas flow measurement calculation. In thepresent embodiment, the timestamp for a first sample is taken from thesystem clock. Subsequent to that, a timestamp for a sample is derived bycounting the number of oscillator ticks that have transpired since theprevious sample was produced, computing the elapsed time based on thenumber of ticks counted, and adding the elapsed time to the time-stampof the previous sample. Thus, the first timestamp will be a currentdate/time from the system clock, and subsequent timestamps will berelative to that first timestamp but accurately spaced according to theoscillator. In the preferred embodiment, the hardware oscillator is theADC clock itself, which ensures that the time-stamps assigned to thepressure samples accurately reflect the relative time in betweensamples.

Over a long duration, the pressure sample time-stamps derived from theoscillator could drift apart from system time, making the gas flowmeasurement data difficult to correlate with other events in the fab. Toresolve this problem, a revised method is employed where the derivedtimestamps are re-synchronized with system time at the beginning of eachgas flow measurement period. In this scenario, the first time-stamp atthe beginning of each gas flow measurement period is taken from thesystem clock, but all subsequent timestamps within the gas flowmeasurement period are derived from the hardware oscillator relative tothe first system timestamp. This ensures that the timestamps during thegas flow measurement period remain accurate relative to each otherwithout system clock jitter or discontinuity, while also ensuring thatthe derived timestamps are effectively re-synchronized with the systemclock at the beginning of each gas flow measurement period. Althoughthis effective resynchronization may cause a small discontinuity in thetimestamps, the discontinuity happens outside of the gas flowmeasurement period where it will not have an impact on the gas flowmeasurements.

FIG. 8 shows a high level flow of the accurate time-stamping method ofdescribed above. At the beginning of a measurement, the first datasample is tagged with the current system timestamp 806. The timestampfor each subsequent sample (814) is derived by: (a) counting the numberof HW ticks that transpired since the last sample was taken, (b) usingthe counted ticks to calculate an elapsed time since the last sample wastaken, and (c) adding the calculated elapsed time to the timestamp ofthe previous sample (816, 818).

The methods described above for accurate time-stamping of pressure datacan also be applied to accurately time-stamp other data that the GFMsystem collects.

Input Data Validation

In some situations, the error in a data sample may be of such amagnitude that it cannot be sufficiently corrected by using the abovemethods. For example, electro-magnetic interference from a nearby system(such as a high power pulse generator) may cause the pressure sensor toproduce faulty data periodically, or a data sample may be corruptedduring transmission to the GFM controller. Even if corrupted datasamples were averaged with other valid samples, the magnitude of theerror in the corrupted samples may still be large enough to materiallyskew the gas flow measurement results. In such situations, it ispreferable to omit the corrupted data from the gas flow measurementcalculation. Embodiments of the present invention allow for performing a“validation check” by applying a heuristic to input samples to determinewhether they are fit to be used in the gas flow measurement calculation.

In one embodiment, an input data sample is compared against a thresholdvalue to perform the validation check. If the data has crossed thethreshold, the data is considered valid. Otherwise, it is discarded. Inan alternate embodiment, the threshold is configured to change overtime. In another embodiment, if the input data fails the validationcheck, the data is substituted with an alternate value (such as anextrapolated sample, a pre-configured constant, the previous value,among other choices) instead of being discarded. In another embodiment,the input data is compared to two thresholds. If the value of the inputdata is in between the two thresholds, the data is considered valid, anddiscarded otherwise. In another embodiment, a validation index iscomputed from multiple input samples using a mathematical formula. Ifthe validation index crosses a threshold, the data is considered valid,and discarded otherwise. In another embodiment, the threshold itself isa mathematically computed value. If the input data crosses the computedthreshold, the data is considered valid, and discarded otherwise. Otherembodiments of the present invention employ a combination of the aboveembodiments to validate input data for gas flow measurement calculation.

Input Data Exclusion

In some situations, there may be periods of time when the input data isknown to be unstable or erroneous, and therefore should be excluded fromthe gas flow measurement calculation. For example, if the rate ofpressure change in volume 114 is suddenly altered, a period of gas flowmeasurement instability might result due to a combination of FCD 118hysteresis and adiabatic expansion in the volume. The rate of pressurechange in the volume can be altered by the FCD changing set points, orthe valve 110 changing states, among other reasons. Initiating a gasflow measurement during such a period of instability (which involvescausing the pressure to drop within the gas stick) can further increasethe pressure instability and negatively affect the stability of the FCD,which can ultimately cause anomalies in the GFM system gas flowmeasurements. Including data during this time period of pressureinstability into the gas flow calculation can result in inaccurate gasflow measurements. Embodiments of the present invention allow forexcluding pressure readings during a time period immediately followingan event that would alter the rate of pressure change in the volume.Such events include but are not limited to a change of the FCD setpoint, a change of the state of the valve, and the initiation of a gasflow measurement. In various embodiments, the time period is hard coded,configurable, or is be calculated based on available data such as FCDset point, pressure readings, and FCD feedback data. Once the timeperiod has passed, the GFM system begins including pressure samples intothe gas flow measurement.

Input Data Precision Enhancement

Embodiments of the present invention also allow for enhancing theeffective bit precision of data in the GFM system in order to improvemeasurement precision. The GFM system receives temperature and pressuredata, either digitally, or in analog form which is then converted todigital format using an ADC. In either case, the data arrives at the GFMcontroller with a pre-determined bit-precision, typically in the 10-18bit range, although in some cases could be outside that range. Eachinput sample is subject to quantization error based on the bit-precisionof the sample. The resulting gas flow measurement will have aquantization error that corresponds to the quantization error in theinput data. In some situations, it is desirable to improve the gas flowmeasurement precision by reducing the quantization error in themeasurement.

In one embodiment, the GFM controller samples input data at a ratefaster than the GFM processing rate. Samples of the input data are thenaveraged to produce a pre-processed sample whose effective bit-precisionis higher than the bit-precision of a single raw input sample,effectively reducing the quantization error in the pre-processed sample.The pre-processed samples are then used for the gas flow calculation,which results in a gas flow measurement of a higher bit-precision thanwould have been computed using un-preprocessed raw samples. Using thismethod, the gas flow calculation formula becomes:

$\begin{matrix}{{f = \frac{\Delta ( {( P_{avg} ){V/{RT}}} )}{\Delta \; t}},{{{where}\mspace{14mu} P_{avg}} = \frac{\sum\limits_{i}P_{i}}{i}}} & {{Equation}\mspace{14mu} (3)}\end{matrix}$

or, when temperature input samples are similarly enhanced,

$\begin{matrix}{{{f = \frac{\Delta( {( P_{avg} ){V/{R( T_{avg} )}}} }{\Delta \; t}},{where}}\text{}{P_{avg} = {{\frac{\sum\limits_{i}P_{i}}{i}\mspace{14mu} {and}\mspace{14mu} T_{avg}} = \frac{\sum\limits_{i}T_{i}}{i}}}} & {{Equation}\mspace{14mu} (4)}\end{matrix}$

To illustrate the concept, consider the extreme example where a GFMsystem is configured to compute gas flow measurements a rate of onceevery 30 ms using 1-bit pressure data that is also sampled at once every30 ms. The resulting gas flow measurement would be based on pressuredata with a precision of 1 bit (i.e., there are only two possiblevalues). However, increasing the raw pressure data input sampling rateto a 10 ms interval (3 times faster than the gas flow measurement outputrate) while keeping the GFM computation rate at 30 ms allows for 3 rawpressure samples to be averaged into a single pre-processed pressuresample before using the pre-processed data to compute a gas flowmeasurement. Averaging three 1-bit raw pressure data samples yields aresulting pre-processed sample with an effective bit-precision of 2 bits(i.e., with four possible values). As a result, the gas flow measurementcalculation benefits from a higher effective bit-precision by samplingand pre-processing the input data at a faster rate than the interval atwhich measurements are computed. In an alternate embodiment, a similarbit-precision enhancement is achieved by averaging multiple GFM outputmeasurements together to produce a single GFM output sample. That is,the GFM processing rate is increased to match the accelerated samplingrate, and the computed results are then averaged to provide output withan increased effective bit precision.

In another embodiment, the effective bit-precision of pressure samplesderived from an ADC is enhanced by applying the full dynamic range ofthe ADC to a subset of the range of possible pressure values. Forexample, a pressure transducer may provide a voltage range of 0-10V,which corresponds to 0-100 psi. Conventionally, the corresponding ADCwould be configured to sample voltages from 0-10V, and map the sampledvalues to the full 0-100 psi range. In this scenario, using a 10-bitADC, pressure values would be quantized to the nearest 0.1 psi. Whenmeasuring a low flow situation where the pressure drops very slowly overtime, a 0.1 psi quantization error on the pressure data could produce asizeable percentage error in gas flow measurement. In the presentembodiment of the invention, the quantization noise can be minimized byadjusting the voltage range of the ADC to only include the range ofvoltages that correspond to the pressure range that is expected in thevolume 114. For example, if the range of pressure values in volume 114is expected to stay between 30 psi and 40 psi, the ADC configuration ismodified to apply its full dynamic range to 3-4V instead of theconventional 0-10V. By applying the full 10-bits across a range of 1Vinstead of 10V, the quantization error is reduced to 0.01 psia, tentimes more precise than when this method is not employed.

Similar bit-precision enhancements for other data collected by the GFMsystem can be achieved using similar methods as described above. Forexample, the effective bit-precision of temperature readings cansimilarly enhanced using the techniques described above.

Measurement Output Enhancement

The methods described above for enhancing gas flow measurement accuracyare applied to input data samples. Embodiments of the present inventionalso allow for further enhancing GFM measurements by varying thepressure slope calculation formula for calculating flow rates. Equation(2) describes the method for computing gas flow rate. Given V and R areconstants, and assuming T does not change materially in a small timeframe (and therefore can be modeled as a constant for the purposes ofdemonstrating the formula), the equation can be simplified to:

$\begin{matrix}{f = \frac{\Delta \; {P( \frac{V}{RT} )}}{\Delta \; t}} & {{Equation}\mspace{14mu} (5)}\end{matrix}$

That is, the flow rate is calculated by computing a scaled “slope” ofthe pressure. In the basic form, slope is calculated across two pressuresamples with the formula:

$\begin{matrix}{{slope} = {\frac{\Delta \; P_{i}}{\Delta \; t_{i}} = \frac{( {P_{i} - P_{i - 1}} )}{( {t_{i} - t_{i - 1}} )}}} & {{Equation}\mspace{14mu} (6)}\end{matrix}$

where t_(i) is the timestamp associated with the pressure sample P_(i).The slope is then scaled by (VIRT) to compute the gas flow rate.Although the above formula is generally effective in computing a flowrate, it may contain artificial errors based on quantization error orother noise in the pressure readings. To minimize the magnitude of theseerrors, the gas flow measurement formula can be enhanced to providebetter accuracy.

In one embodiment, the slope of pressure is calculated using a linearfit across a time window that contains more than 2 pressure samples,using a least squares algorithm or similar. Enhancing Equation (6) toinclude a least squares linear fit over N data points, we get:

$\begin{matrix}{{slope} = {\frac{\Delta \; P_{i}}{\Delta \; t_{i}} = \frac{{N{\sum\limits_{a = 0}^{N - 1}( {P_{i - a}t_{i - a}} )}} - {( {\sum\limits_{b = 0}^{N - 1}P_{i - b}} )( {\sum\limits_{c = 0}^{N - 1}t_{i - c}} )}}{( {N{\sum\limits_{d = 0}^{N - 1}( P_{i - d} )^{2}}} )( {N{\sum\limits_{e = 0}^{N - 1}( t_{i - e} )^{2}}} )}}} & {{Equation}\mspace{14mu} (7)}\end{matrix}$

By using a larger set of pressure samples to compute a linear fit,variance of the slope is effectively reduced. Employing a linear fitformula also has a side effect of causing a delay in the gas flowmeasurement output. To counteract that delay, in another embodiment, thenumber pressure samples in the window is varied over time to minimizethe output delay. For example, the first output sample is computed usinga window containing only two pressure samples. The next output sample iscomputed using a window containing three pressure samples, and so on,until a configurable input sample limit has been reached. Once the limitis reached, subsequent output samples are computing using the samenumber pressure samples as the previous output sample until the gas flowmeasurement period ends.

In another embodiment, the gas flow measurement output data is itselfaveraged over a window containing multiple gas flow measurement point tofilter out noise in the measurement. The size of the averaging window isproportional to the delay in measurement output, which can becounteracted using a similar method as described previously of growingthe window over time. If the GFM system is configured to process datafaster than the desired output granularity, the output can be averagedwithout incurring a delay in the measurement output.

Variable Gas Compressibility

In Equation (5) above, the gas flow is modeled as a scaled pressureslope, because V/RT is modeled as a constant. However, as taught byMonkowski, the ideal gas constant R does not behave like a constantbecause gases used for semiconductor processing are all real (non-ideal)to some extent.

So although Equation (5) is sufficient to provide a gas flowmeasurement, the accuracy of the gas flow measurement can be enhanced byadjusting the equation to match the behavior of each real gas beingmeasured. Thus Equation (1) can be expanded to:

n=PV/ZRT, where   Equation (8)

n=amount of gas

P=pressure

V=volume

Z=gas compressibility factor

R=ideal gas constant

T=temperature

Expanding Equation (5) to account for Z, we get:

$\begin{matrix}{f = \frac{\Delta \; {P( \frac{V}{ZRT} )}}{\Delta \; t}} & {{Equation}\mspace{14mu} (9)}\end{matrix}$

The gas compressibility factor Z is used to account for the behavior ofthe real gas being delivered by the gas stick. At first glance, onecould surmise that each gas stick only delivers a single gas to theprocess chamber, so that once Z is determined for that gas, it can betreated as a constant for gas flow calculation purposes on that gasstick. Although treating Z as a constant is sufficient for estimatingthe gas flow rate in some situations, a higher accuracy can be obtainedby treating Z as a variable instead of a constant. It is well known inthe art that Z generally increases with pressure and decreases withtemperature in a non-linear fashion. Therefore, since Z variesnon-linearly as a function of pressure and temperature, modeling theflow as a scaled pressure slope as indicated in Equation (9) will yielda gas flow measurement that drifts non-linearly over time (sincepressure and temperature change over time during the gas flowmeasurement). To correct that drift, the slope calculation formula isre-written as:

$\begin{matrix}{f = \frac{{\Delta ( \frac{P}{Z_{P,T}} )}( \frac{V}{RT} )}{\Delta \; t}} & {{Equation}\mspace{14mu} (10)}\end{matrix}$

treating T as a constant in order to simplify the equation to illustratethe innovation related to Z. In Equation (10) above, one can see how tothe compressibility factor Z is a function of pressure and temperature,and can affect the gas flow rate f. Empirically, the resulting flowcalculation from Equations (5) and (9) may appear non-linear over time,whereas correcting with Z as shown in Equation (10) compensates for thatinherent non-linearity. Therefore, a more accurate flow measurement canbe obtained by performing a linear fit over the change in moles (whichare Z-corrected) instead of doing the linear fit over the change inpressures (which are not inherently Z-corrected). Enhancing Equation(10) to provide for a linear fit over N mole data points using the leastsquares method yields:

$\begin{matrix}{{{f = \frac{{N{\sum\limits_{a = 0}^{N - 1}( {n_{i - a}t_{i - a}} )}} - {( {\sum\limits_{b = 0}^{N - 1}n_{i - b}} )( {\sum\limits_{c = 0}^{N - 1}t_{i - c}} )}}{( {N{\sum\limits_{d = 0}^{N - 1}( n_{i - d} )^{2}}} )( {N{\sum\limits_{e = 0}^{N - 1}( t_{i - e} )^{2}}} )}},{where}}\text{}{n_{i} = \frac{P_{i}V}{Z_{i}{RT}_{i}}}} & {{Equation}\mspace{14mu} (11)}\end{matrix}$

Embodiments of the present invention allow for dynamically adjusting thegas compressibility factor Z during the course of gas flow measurement,to account for the changes in pressure and temperature occurring duringthe gas flow measurement. In one embodiment, Z is obtained from alook-up table using pressure as a look-up index to determine thecompressibility factor at the measured pressure and temperature. In thisembodiment, the GFM software takes a pressure measurement andtemperature measurement and uses them to look up a corresponding gascompressibility factor in the look-up table. If an index for themeasured pressure does not exist, the closest match or an interpolationcan be performed to determine the compressibility factor to be used inthe gas flow calculation. The data in the lookup table can be derivedeither through empirical observation, or by using readily availablecompressibility charts where they exists for the gases being measured.In a related embodiment, the look-up table may only use pressure as alook-up index, and assume temperature to be relatively constant.

In another embodiment, the gas compressibility factor is dynamicallycomputed at the time of gas flow measurement using a mathematicalformula. The formula models the gas compressibility as a function ofpressure and temperature. In this embodiment, the GFM software takes apressure reading and temperature reading, and uses them to compute thecompressibility factor for the gas using the pressure and temperaturereadings. In a related embodiment, the formula assumes a constanttemperature so only a pressure reading is required to compute the gascompressibility factor. In another embodiment, the mathematical formulauses configurable coefficients in order to use the same formula (withdifferent coefficients) across multiple gas sticks, reducing the need tocode separate formulas in the GFM software.

While the above description has focused upon the use of the invention inconnection with a gas stick for a semiconductor processing chamber,embodiments in accordance with the present invention are not limited touses in the semiconductor industry. Other industries in which thisinvention may be applicable include but are not limited to themanufacture of plasma and liquid crystal displays, solar panelmanufacturing, industrial diamond manufacturing, and other industriesemploying tools similar to those used in semiconductor manufacturing.

It is also understood that the examples and embodiments described hereinare for illustrative purposes only and that various modifications orchanges in light thereof will be suggested to persons skilled in the artand are to be included within the spirit and purview of this applicationand scope of the appended claims.

1. The method of computing the rate at which gas flows out of aprocessing chamber gas stick, the method comprising: stopping the flowof gas into the gas stick at a first location which is upstream of asecond location where gas is flowing out of the gas stick, obtaining aplurality of measurements of the gas in a volume in fluid communicationwith, and located in between, said first and second gas stick locations,deriving time-stamps for said measurements, performing a gas flowcalculation, where the gas flow calculation includes using at least twomeasurements and their corresponding derived time-stamps to compute therate of gas flow out of said volume by calculating the rate of decreasein moles of the gas in the volume using a derivative of the ideal gaslaw, and providing the results of the gas flow calculation via a systeminterface.
 2. The method in claim 1, where the time-stamps are derivedfrom a software clock.
 3. The method in claim 1, where the time-stampsare derived from a hardware oscillator.
 4. The method in claim 1, wherethe timestamp of a measurement is derived by adding a number to thetime-stamp of the previous measurement, where said number is an estimateof the time elapsed since the previous measurement was sampled.
 5. Themethod in claim 4 where said estimate of elapsed time is computed bycounting ticks on a hardware oscillator.
 6. The method in claim 5 wheresaid hardware oscillator is the sampling clock of the ADC that issampling the measurements.
 7. The method in claim 4 where a firstmeasured sample at the beginning of a measurement period is set to thesystem time of when the sample was received.
 8. The method in claim 1,wherein said measurements are taken from a pressure sensor.
 9. Themethod in claim 1, wherein said measurements are taken from atemperature sensor.
 10. The method in claim 1, wherein providing theresults of the gas flow calculation via a system interface comprisessending an analog voltage signal over a conductor.
 11. The method inclaim 1, wherein providing the results of the gas flow calculation via asystem interface comprises sending a digital signal over a digitalinterface.
 12. The method in claim 1, wherein providing the results ofthe gas flow calculation via a system interface comprises storing a fileon a computer-readable medium.
 13. The method of computing the rate atwhich gas flows out of a processing chamber gas stick, the methodcomprising: stopping the flow of gas into the gas stick at a firstlocation which is upstream of a second location where gas is flowing outof the gas stick, obtaining a plurality of measurements of the gas in avolume in fluid communication with, and located in between, said firstand second gas stick locations, obtaining compressibility factors of thegas that correspond to the values of said measurements, scaling saidmeasurements by their corresponding compressibility factors, performinga gas flow calculation, where the gas flow calculation includes using atleast two scaled measurements to compute the rate of gas flow out ofsaid volume by calculating the rate of decrease in moles of the gas inthe volume using a derivative of the ideal gas law, and providing theresults of the gas flow calculation via a system interface.
 14. Themethod in claim 13, where the compressibility factor for a measurementis obtained from a lookup table.
 15. The method in claim 13, where thecompressibility factor for a measurement is obtained by computing avalue using a mathematical formula.
 16. The method in claim 13, where alinear fitting formula is used to compute said rate of decrease inmoles.
 17. The method in claim 13, wherein said measurements are takenfrom a pressure sensor.
 18. The method in claim 13, wherein saidmeasurements are taken from a temperature sensor.
 19. The method inclaim 13, wherein providing the results of the gas flow calculation viaa system interface comprises sending an analog signal over a conductor.20. The method in claim 13, wherein providing the results of the gasflow calculation via a system interface comprises sending a digitalsignal over a digital interface.
 21. The method in claim 13, whereinproviding the results of the gas flow calculation via a system interfacecomprises storing a file on computer-readable medium.
 22. A gas flowmeasurement system coupled to a gas stick in fluid communication with aprocessing chamber, the gas stick comprising a flow control device onthe gas stick located upstream of the processing chamber, a valve, onthe gas stick, located upstream of the flow control device, which hasthe ability to regulate the flow of gas through the gas stick, and avolume in fluid communication with, and located in between, the valveand the flow control device, the system comprising: one or more sensorsin fluid communication with, and located in between, the valve and theflow control device, and, a computer, in electronic communication withsaid sensors, and which comprises: a processor, a computer-readablemedium having stored thereupon a program that, when executed on saidprocessor causes the processor to perform the steps: stop the flow ofgas into the gas stick by turning off the valve, obtain compressibilityfactors of the gas that correspond to the values of said measurements,scale said measurements by their corresponding compressibility factors,perform a gas flow calculation, where the gas flow calculation includesusing at least one scaled measurement to compute the rate of gas flowout of said volume by calculating the rate of decrease in moles of thegas in the volume using a derivative of the ideal gas law, and providethe results of the gas flow calculation via a system interface.